I created a new project and started making new statuses and transitions, however, these new statuses/transitions are now replacing the statuses/transitions in the other projects. How can I avoid this?

[Nic Brough -Adaptavist-]

You'll find the projects share the same workflow scheme, so when you change a workflow in that scheme, it affects all projects using it.  You can decouple this - create a new workflow scheme, with its own workflows (copying them is an excellent approach) and set the projects to use different ones.